2026/04/08 by Bernd von Mallinckrodt · 1 voice
Economics, Econometrics and Finance · Environmental Science · Physics and Astronomy · #Chaos control and synchronization #Complex Systems and Time Series Analysis #Ecosystem dynamics and resilience
paper · doi:10.5281/zenodo.19469862
openalex publication_date 2026/04/08 · openalex created_date 2026/04/09 · openalex updated_date 2026/07/01
This preprint introduces structural compression Φ(t), defined as the exponential spectral entropy of a rolling covariance matrix, as a mechanism-specific early warning signal for critical transitions in multivariate systems. While classical early warning indicators such as variance and lag-1 autocorrelation capture amplitude and temporal memory, respectively, they do not detect changes in the geometric structure of covariance. Φ(t) addresses this gap by measuring the effective dimensionality of the system and identifying the concentration of variance into dominant modes. The framework is extended through the Compression–Response Transition Index (CRTI), defined as T(t) = R(t) / Φ(t), where R(t) is an adaptive response proxy derived from autoregressive dynamics. A Structural–Dynamic Separability (SDS) condition is introduced as a validity constraint, ensuring that structural and dynamic components contribute distinguishable information before combination. The approach is empirically evaluated using S&P 500 sector ETF return data over the period 2004–2008. Results show a sustained decline in Φ(t) beginning approximately 12–18 months prior to the 2008 financial crisis, while classical early warning indicators exhibit no statistically consistent precritical trend under identical estimation conditions. Surrogate testing using IAAFT methods demonstrates that the observed Φ(t) trend cannot be explained by the linear autocorrelation structure of the data, indicating the presence of higher-order structural dynamics. These findings support the interpretation of covariance geometry as a distinct dimension of precritical behavior and provide a formally specified, testable framework for its measurement. The CRTI approach is explicitly mechanism-specific and is not proposed as a universal early warning signal, but as a complementary tool for systems where structural compression precedes dynamic slowing. Structural Compression; Early Warning Signals; Critical Transitions; CRTI; Spectral Entropy; Covariance Structure; Effective Dimensionality; Complex Systems; Financial Markets; Systemic Risk; Fold Bifurcation; Multivariate Time Series; Random Matrix Theory; Surrogate Testing; IAAFT